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JEE Main202226 Jul 2022Morning ShiftMathematicsVector AlgebraActual

Let a → = α i ^ + j ^ - k ^ and b → = 2 i ^ + j ^ - α k ^ , α > 0 . If the projection of a → × b → on the vector - i ^ + 2 j ^ - 2 k ^ is 30 , then α is equal to

Options

  1. A15 2
  2. B8
  3. C13 2
  4. D7

Correct answer

D. 7

Step-by-step solution

Given, a → = α i ^ + j ^ - k ^ and b → = 2 i ^ + j ^ - α k ^ , α > 0 . If the projection of a → × b → on the vector - i ^ + 2 j ^ - 2 k ^ is 30 , then α is equal to Now a → × b → = i ^ j ^ k ^ α 1 - 1 2 1 - α = 1 - α i ^ + α 2 - 2 j ^ + α - 2 k ^ Projection of a → × b → on - i ^ + 2 j ^ - 2 k ^ = a → × b → · - i ^ + 2 j ^ - 2 k ^ 1 2 + 2 2 + 2 2 = 1 - α i ^ + α 2 - 2 j ^ +

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